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Topological Data Analysis

arXiv 1609.08227 ↗First posted 27 Sep 2016stat.MEcited by 16

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Abstract (arXiv)

Topological Data Analysis (TDA) can broadly be described as a collection of data analysis methods that find structure in data. This includes: clustering, manifold estimation, nonlinear dimension reduction, mode estimation, ridge estimation and persistent homology. This paper reviews some of these methods.

Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). First posted on arXiv 27 Sep 2016.

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Citing papers per year: 2021: 4; 2022: 3; 2023: 4; 2024: 3; 2025: 1; 2026: 1.

16 papers.

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  1. 2022Scalable algorithms for physics-informed neural and graph networkscited by 21
  2. 2023The Topology and Geometry of Neural Representationscited by 13
  3. 2021Tangent Space and Dimension Estimation with the Wasserstein Distancecited by 10
  4. 2025Topological Signatures vs. Gradient Histograms: A Comparative Study for Medical Image Classificationcited by 10
  5. 2021Topological Measurement of Deep Neural Networks Using Persistent Homologycited by 9
  6. 2022Enhancing cluster analysis via topological manifold learningcited by 6
  7. 2022UDRN: Unified Dimensional Reduction Neural Network for Feature Selection and Feature Projectioncited by 5
  8. 2024Persistent de Rham-Hodge Laplacians in Eulerian representation for manifold topological learningcited by 3
  9. 2021Joint Geometric and Topological Analysis of Hierarchical Datasetscited by 1
  10. 2023Can Persistent Homology provide an efficient alternative for Evaluation of Knowledge Graph Completion Methods?cited by 1
  11. 2023Generalized partitioned local depthcited by 1
  12. 2023Topological data analysis of human vowels: Persistent homologies across representation spacescited by 1
4 more
  1. 2021Statistical embedding: Beyond principal componentscited by 0
  2. 2024PlasmoData.jl -- A Julia Framework for Modeling and Analyzing Complex Data as Graphscited by 0
  3. 2024A cohomology-based Gromov-Hausdorff metric approach for quantifying molecular similaritycited by 0
  4. 2026Beyond Distance: Quantifying Point Cloud Dynamics with Persistent Homology and Dynamic Optimal Transportcited by 0